\xiti
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\begin{xiaotis}

\xiaoti{通分：}
\begin{xiaoxiaotis}

    \begin{tblr}{columns={18em, colsep=0pt}, rows={rowsep+=.25em}}
        \xxt{$\dfrac{4}{3x} \nsep \dfrac{x-1}{-2x^2} \nsep \dfrac{x+1}{4x^3}$；} & \xxt{$\dfrac{x}{a(x - y)} \nsep \dfrac{y}{b(y - x)}$；} \\
        \xxt{$\dfrac{1}{(2 - x)^2} \nsep \dfrac{x}{(x+2)(x-2)}$；} & \xxt{$\dfrac{a+b}{(a-b)(b-c)} \nsep \dfrac{b+c}{(b-c)(b-a)}$；} \\
        \xxt{$\dfrac{x}{x^2-x-2} \nsep \dfrac{1}{x-2}$；} & \xxt{$\dfrac{a}{a^3-b^3} \nsep \dfrac{1}{a^2-b^2}$；} \\
        \SetCell[c=2]{} \xxt{$\dfrac{x+4}{x^2-8x+15} \nsep \dfrac{x-5}{x^2+x-12} \nsep \dfrac{x-3}{x^2-x-20}$；} \\
        \xxt{$\dfrac{1}{(x-1)^2} \nsep \dfrac{x}{x^3-1}$。}
    \end{tblr}

\end{xiaoxiaotis}

\xiaoti{下列各式的计算对不对？把不对的改正过来：}
\begin{xiaoxiaotis}

    \xxt{$\dfrac{c-d}{a} - \dfrac{c+d}{a} = \dfrac{c-d-c+d}{a} = \dfrac{0}{a} = 0$；}

    \xxt{$\dfrac{x}{(x-1)^2} + \dfrac{1}{(1-x)^2} = \dfrac{x}{(x-1)^2} - \dfrac{1}{(x-1)^2} = \dfrac{x-1}{(x-1)^2} = \dfrac{1}{x-1}$。}

\end{xiaoxiaotis}

\xiaoti{计算：}
\begin{xiaoxiaotis}

    \xxt{$\dfrac{1}{6x-4y} - \dfrac{1}{6x+4y} - \dfrac{2y}{9x^2-4y^2}$；}

    \xxt{$\dfrac{1}{x^2+3x+2} + \dfrac{1}{x^2+5x+6} + \dfrac{1}{x^2+4x+3}$；}

    \xxt{$x^2+x+1 - \dfrac{x^3}{x-1}$；}

    \xxt{$x + 2y + \dfrac{4y^2}{x-2y} + \dfrac{4x^2y}{4y^2-x^2}$；}

    \xxt{$\left(x - y + \dfrac{4xy}{x-y}\right)\left(x + y - \dfrac{4xy}{x+y}\right)$；}

    \xxt{$\left[\dfrac{1}{(a+b)^2} - \dfrac{1}{(a-b)^2}\right] \div \left(\dfrac{1}{a+b} - \dfrac{1}{a-b}\right)$；}

    \xxt{$\dfrac{x}{x-y} \cdot \dfrac{y^2}{x+y} - \dfrac{x^4y}{x^4-y^4} \div \dfrac{x^2}{x^2+y^2}$；}

    \xxt{$\dfrac{3x-2}{x^2-x-2} + \left(1-\dfrac{1}{x+1}\right) \div \left(1 + \dfrac{1}{x-1}\right)$。}

\end{xiaoxiaotis}

\xiaoti{化简：}
\begin{xiaoxiaotis}

    \threeInLineXxt{$\dfrac{\dfrac{y^3-1}{y}}{\enspace \dfrac{y^2-1}{y} \enspace}$；}
                   {$\dfrac{\dfrac{1}{a} + \dfrac{1}{b}}{1 - \dfrac{1}{ab}}$；}
                   {$\dfrac{\dfrac{x+1}{x-1} - \dfrac{x-1}{x+1}}{\dfrac{1}{x^2-1}}$。}

\end{xiaoxiaotis}

\xiaoti{锅炉房储存了 $t$ 天用的煤 $m$ 吨。要使储存的煤比预定的多用 $d$ 天，每天应当节约多少吨？}

\xiaoti{一架幻灯机，当镜头与幻灯片之间的距离是 $S$（ 厘米）时，幻灯片上景物长度放大的倍数是
    $\dfrac{\dfrac{1}{S}}{\dfrac{1}{18} - \dfrac{1}{S}}$。
    先化简这个繁分式，然后求出当 $S = 20$ 厘米时景物长度放大的倍数。
}

\end{xiaotis}

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